Communications in Mathematical Physics

, Volume 246, Issue 3, pp 453–472

Equivalence of Additivity Questions in Quantum Information Theory

  • Peter W. Shor

DOI: 10.1007/s00220-003-0981-7

Cite this article as:
Shor, P. Commun. Math. Phys. (2004) 246: 453. doi:10.1007/s00220-003-0981-7


We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Peter W. Shor
    • 1
    • 2
  1. 1.AT & Labs ResearchUSA
  2. 2.Dept. of MathematicsMassachusetts Institute of TechnologyUSA

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